Posted by **John** on Thursday, May 16, 2013 at 7:21pm.

Let S be the set of {(1,1),(1,−1),(−1,1)} -lattice path which begin at (1,1) , do not use the same vertex twice, and never touch either the x -axis or the y -axis. Determine the largest value of n such that every path in S which ends at (n,n) has length at most 50000 .

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